{"paper":{"title":"On strict Whitney arcs and $t$-quasi self-similar arcs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GN"],"primary_cat":"math.MG","authors_text":"Daowei Ma, Xin Wei, Zhiying Wen","submitted_at":"2017-03-30T20:33:39Z","abstract_excerpt":"A connected compact subset $E$ of $\\mathbb{R}^N$ is said to be a strict Whitney set if there exists a real-valued $C^1$ function $f$ on $\\mathbb{R}^N$ with $\\nabla f|_E\\equiv 0$ such that $f$ is constant on no non-empty relatively open subsets of $E$. We prove that each self-similar arc of Hausdorff dimension $s>1$ in $\\mathbb{R}^N$ is a strict Whitney set with criticality $s$. We also study a special kind of self-similar arcs, which we call \"regular\" self-similar arcs. We obtain necessary and sufficient conditions for a regular self-similar arc $\\Lambda$ to be a $t$-quasi-arc, and for the Hau"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10665","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}